Barnes Jonathan. Truth, etc

Подождите немного. Документ загружается.

150 Predicates and Subjects

That diagnosis gives the required results in the case of the three arguments

before us. But it is difﬁcult to see how anyone who was not beguiled by

the Categories could have thought that it was a plausible diagnosis, or that

it was the only or the best way to exclude the fallacious inferences. For

quite apart from anything else, it has disastrous consequences for Aristotle’s

syllogistic—as the passage I quoted from Simplicius well illustrates. It

implies—to take another example—that the following argument,

All men can laugh

No crocodiles can laugh

So no men are crocodiles

is not a syllogism in Cesare. And it thus places severe and unwarranted

restrictions on the scope of the syllogistic.

In any event, a better diagnosis of the fallacies in arguments (2) and (3) is not

far to seek. In argument (2), the sentence ‘Grey is a colour’ does not predicate

‘colour’ afﬁrmatively and universally of ‘grey item’. (Why not? Why shouldn’t

I construe it as saying that every grey item is a colour?—Well, construe it like

that if you like; and argument (2) will indeed be valid—but its second premiss

will be false.) Again, the sentence ‘The cat is a species’ does not predicate

‘species’ afﬁrmativelyand universally of ‘cat’. (Again, if you perversely construe

it in that sense, argument (3) is valid—and its second premiss is false.) And

that is all there is to say—transitivity has nothing to do with the case.

That diagnosis was not unknown in antiquity. Here is a passage from

Philoponus’ commentary on the Prior Analytics which proposes it—or half

proposes it.

The article and the universal determiner do not mean the same thing in propositions.

For when I say

Jeoffry is a cat, The cat is an animal,

‘the cat’ signiﬁes the indivisible species of cat, in virtue of which all individual cats

are called cats. But when I say

Every cat is an animal,

I no longer take the indivisible species but rather all the individuals of which the

species holds. That this is true is clear from the fact that you can say

The cat is a species,

but not

Every cat is a species.

Hence the fallacies:

The swan is white

White is a colour

The Transitivity of Predication 151

So the swan is a colour.

For it is not true to say

Every white item is a colour.

For ‘every’ signiﬁes the individuals which participate in white; and you can’t say of

them that they are a colour. But when I say ‘white’, since I take the species white,

it is true to say that it is a colour. So that since the universal premiss is false, the

conclusion too is false.

(in APr 325.26–326.5)⁶⁵

(Philoponus’ examples concern men rather than cats; but in English it is

‘man’ rather than ‘the man’ which names the species.)

The gist of the matter is this. Consider the following argument:

Jeoffry is a cat

The cat is a species

So Jeoffry is a species

The deﬁnite article in the second premiss ensures that the phrase ‘the cat’

designates an indivisible species. The premiss does not mean

Every cat is a species.

It does not do so because, in general, articles and determiners (or quantiﬁers)

do not mean the same thing. Since the second premiss does not mean that

every cat is a species, the argument is not valid—or at any rate, it is not a

valid Aristotelian syllogism.

Philoponus is fundamentally right; and he does not make any reference

to predication-as-of-a-subject, or to essential or synonymous predication.

But he is only half right; for he holds that the phrase ‘the cat’ designates a

species in

The cat is an animal.

That sentence is therefore not equivalent to

Every cat is an animal.

Hence the argument

⁶⁵ οὐ γὰρ ταὐτὸν δύναται ἐν ταῖς προτάσεσι τό τε ἄρθρον καὶ ὁ καθόλου προσδιορισμός.

ὅταν μὲν γὰρ εἴπω Σωκράτης ἄνθρωπος, ὁ ἄνθρωπος ζῷον, τὸ ὁ ἄνθρωπος τὸ ἑνοειδές τοῦ

ἀνθρώπου εἶδος σημαίνει, καθ ᾿ ὃ πάντες οἱ κατὰ μέρος ἄνθρωποι λέγονται· ὅταν δὲ εἴπω

πᾶς ἄνθρωπος ζῷον, οὐκέτι τὸ εἶδος λαμβάνω τὸ ἑνοειδὲς ἀλλὰ τοὺς καθ ᾿ ἕκαστα πάντας

οἷς ὑπάρχει τὸ εἶδος. καὶ ὅτι τοῦτο ἀληθές ἐστι, δῆλον ἐξ ὧν δυνατὸν εἰπεῖν ὁ ἄνθρωπος

εἶδός ἐστιν, οὐ μέντοι πᾶς ἄνθρωπος. ἔνθεν καὶ οἱ παραλογισμοὶ ἐκεῖνοι· ὁ κύκνος λευκός, τὸ

λευκὸν χρῶμα, ὁ κύκνος ἄρα χρῶμα. οὐκέτι γὰρ ἀληθὲς εἰπεῖν πᾶν λευκὸν χρῶμα· τὸ γὰρ

πᾶν τὰ καθ ᾿ ἕκαστα σημαίνει τὰ τοῦ λευκοῦ μετέχοντα· οὐκ ἔστι δὲ ἀληθές εἰπεῖν περὶ τούτων

ὅτι χρῶμά εἰσιν. ὅταν δὲ τὸ λευκὸν εἴπω, ἐπειδὴ τὸ εἶδος τοῦ λευκοῦ λαμβάνω, ἀληθές εἰπεῖν

ὅτι χρῶμά ἐστιν. ὥστε ἐπειδὴ ἡ καθόλου πρότασις ψευδής, καὶ τὸ συμπέρασμα ψευδές.

152 Predicates and Subjects

Jeoffry is a cat

The cat is an animal

So Jeoffry is an animal

is not a valid Aristotelian syllogism—it is just as bad as the previous argument.

But the argument surely is valid; and its second premiss surely is equi-

valent to

Every cat is an animal.

Several ancient texts, logical and grammatical, recognize that in Greek the

deﬁnite article sometimes functions as a universal quantiﬁer, that ‘the so-and-

so’ sometimes means ‘every so-and-so’. Philoponus has no reason—and no

need—to deny that truth.

Again, when Philoponus comments on the Categories he follows the

orthodox line. Predication-as-of-a-subject is transitive.

What does he mean by ‘as of a subject’?—‘Essentially and objectually’; for if

something is predicated accidentally of the predicate it is not necessarily also said of

the subject.

(in Cat 38.28–31)⁶⁶

If x is predicated accidentally of y and y is predicated of z, it does not follow

that x is predicated of z.

The passage in the Categories about the predication of names and their

deﬁnitions is a slip on Aristotle’s part. It is a fairly trivial slip—you can cut the

offending lines from the text and nothing much else will need changing. Nor

did the slip have any effect on anything which Aristotle said in the Analytics.

Nonetheless, once the passage in the Categories was taken to convey a truth,

and a doctrinal truth, and once the Categories became the ﬁrst element in the

Organon, the trivial slip inﬂated into a massive blunder. Whoever invented

the Organon has something to answer for.

Some scholars think that the inventor of the Organon was Andronicus

of Rhodes. Whether or not that is so, Andronicus was not misled—or not

wholly misled—by the trivial slip in the Categories. Simplicius says:

It should be noted that Andronicus, and also some others, say that it is not only items

predicated essentially which are predicated of a subject—so too are other items:

for example, ‘musical’ of Aristoxenus, and ‘Athenian’ of Socrates, and perhaps those

items in predicating which of something we say that it is just what we predicate—in

⁶⁶ τί δὲ αὐτῷ βούλεται τὸ ὡς καθ ᾿ ὑποκειμένου; τὸ οὐσιωδῶς καὶ πραγματικῶς· εἰ γάρ τι

κατὰ τοῦ κατηγορουμένου κατὰ συμβεβηκὸς κατηγορεῖται, οὐκ ἀνάγκη τοῦτο καὶ κατὰ τοῦ

ὑποκειμένου λέγεσθαι.

The Transitivity of Predication 153

saying that Socrates walks we do not say that Socrates is walks, but we do say that he is

Athenian and a philosopher. And what is predicated of those items, when we say that

they are such-and-such, will also be said of the subject. For if Socrates is a philosopher

and a philosopher is knowledgeable, then Socrates too will be knowledgeable. Again,

they say: if a body is white and white is a colour, will a body then be a colour? Surely

white signiﬁes two things, the quality and also what is coloured? It is what is coloured

which is predicated of the body (for the body is not whiteness), whereas it is the colour

which is predicated of the quality (for the quality is not whitened but whiteness).

Thus it is not the colour but the coloured item which is predicated of the body.

(in Cat 54.8–21)⁶⁷

That is all we know about Andronicus’ view—and the text at the very

end of the passage is uncertain. Even so, it is plain that Andronicus gave a

good diagnosis of Aristotle’s example of ‘white’. As for Andronicus’ general

position, Simplicius is not as clear as he might have been: plainly, he did not

think much of it, and he reported it dutifully rather than excitedly.

Nonetheless, the illustrative examples suggest something like this. Andro-

nicus agrees with Aristotle that predication is not, in general, transitive:

rather, it is predication-as-of-a-subject which is transitive. But predication-

as-of-a-subject is not limited to essential predication. It is found not only in

the essential sentence

Socrates is a man,

but also in the accidental

Socrates is Athenian.

And surely the same goes for all predication? Not according to Simplicius’

text; for the text indicates that predication-as-of-a-subject occurs with ‘those

itemsinpredicatingwhichofsomethingwesaythatitisjustwhatwe

predicate’. So predication-as-of-a-subject is not found in (say)

Socrates walks

—for when we say that Socrates walks we do not say that Socrates is walks.

⁶⁷ ἰστέον δὲ ὅτι καὶ ᾿Ανδρόνικος καὶ ἄλλοι δέ τινες οὐ μόνον τὰ ἐν τῷ τί ἐστι κατηγορούμενα

καθ ᾿ ὑποκειμένου κατηγορεῖσθαί φασιν, ἀλλὰ καὶ ἄλλα οἷον τὸ μουσικὸν κατὰ ᾿Αριστοξένου

καὶ τὸ ᾿Αθηναῖος κατὰ Σωκράτους, καὶ ἴσως ἐκεῖνα ὅσα κατηγοροῦντές τινος ἐκεῖνο εἶναι

λέγομεν αὐτὸ ὅπερ κατηγοροῦμεν· βαδίζειν μὲν γὰρ λέγοντες τὸν Σωκράτη οὐ λέγομεν

βαδίζειν εἶναι τὸν Σωκράτη, ᾿Αθηναῖον δὲ εἶναι λέγομεν καὶ φιλόσοφον. καὶ ὅσα δὴ τούτων

κατηγορεῖται, λεγόντων ἡμῶν ταῦτα ἐκεῖνα εἶναι, καὶ κατὰ τοῦ ὑποκειμένου ῥηθήσεται·

εἰ γὰρ ὁ Σωκράτης φιλόσοφος καὶ ὁ φιλόσοφος δὲ ἐπιστήμων, ἔσται καὶ ὁ Σωκράτης

ἐπιστήμων. πάλιν δέ φασιν· εἰ τὸ σῶμα λευκὸν καὶ τὸ λευκὸν χρῶμα, ἔσται καὶ τὸ σῶμα

χρῶμα; ἢ τὸ λευκὸν δύο σημαίνει, τήν τε ποιότητα καὶ τὸ κεχρωσμένον, καὶ τοῦ μὲν

σώματος τὸ κεχρωσμένον κατηγορεῖται (οὐ γάρ ἐστι τὸ σῶμα λευκότης), τῆς δὲ ποιότητος

τὸ χρῶμα, (<οὐ γάρ ἐστιν ἡ ποιότης λελευκωμένον> ἀλλὰ λευκότης)· ὥστε οὐ τὸ χρῶμα

κατηγορηθήσεται τοῦ σώματος, ἀλλὰ τὸ κεχρωσμένον.

154 Predicates and Subjects

Yet I wonder if Andronicus meant to restrict predication-as-of-a-subject in

that way—or in any other way. When Simplicius says ‘and perhaps those items

in predicating which …’ he seems to me not to be reporting a generalization

which Andronicus had made but rather to be conjecturing a generalization

of his own. And the conjecture seems to me to be rather dubious, for the

following reason. I have already invoked the Aristotelian thesis that ‘x verbs’

and ‘x is verbing’ are synonymous. That thesis was accepted—so far as I

know—by all ancient Aristotelians, and there is no reason to imagine that

Andronicus raised a dissident voice. So he will have known that

Socrates walks

isthesameas

Socrates is a walking item.

If he thought that

Socrates is Athenian

is a predication-as-of-a-subject, then he must surely have held the same

view of

Socrates is a walking item.

And in that case, every predication either is or is synonymous with a

predication-as-of-a-subject, and the restriction of transitivity to predication-

as-of-a-subject is no restriction at all. In short, Andronicus probably saw that

all predication—that is to say, all A-predication—is transitive.

SINGULAR PREDICATION

But is there not something very wrong with the last few pages of my argument?

I have said that, with the exception of Andronicus, ancient scholars endorsed

the false thesis of the Categories according to which A-predication is not in

general transitive: transitivity is a property of essential A-predication, not of

A-predication itself. But the Categories does not speak of A-predication: it

speaks of predication in general, and it makes no mention of what I have

called different styles of predication.

Not only that: in addition, it seems that the argument in the Categories can-

not be construed in terms of A-predication. For the examples of predication

about which it turns include singular sentences such as

Socrates is white;

and they do not express A-predications. Indeed, according to the modern

wisdom, singular sentences do not convey predications of any Aristotelian

style. They convey, as we might say, singular predications; and singular

Singular Predication 155

predications are not recognized by Aristotle’s syllogistic and hence are not

Aristotelian predications at all.

Singular sentences have long been supposed to raise a problem for Aris-

totelian logic—or to reveal a fundamental weakness in Aristotelian syllogistic.

For on the one hand, it seems evident that if x is predicated of y, then both x

and y must be general terms; or, more precisely, that if x is predicated in style

S of y, and S is one of the four Aristotelian styles, then both x and y must be

general terms. That is implicit in the structure of the syllogistic; and although

it is never discussed or examined by the ancient logicians, it is found more or

less explicitly in a scattering of texts. On the other hand, Aristotle’s followers

and commentators—and also Aristotle himself—sometimes introduce sin-

gular sentences into syllogisms. They do so with no embarrassment. They do

nothintthatsuchitemsareanomalous—orworse.

Their remarkable nonchalance in this regard is explained in part—or so

it is tempting to conjecture—by the inﬂuence of the Categories.Atanyrate,

once you take the Categories and its doctrine of predication to introduce the

logic of the Analytics, and once you think that one of the ﬁrst questions to

be raised about predication is the question of transitivity which is implicitly

tackled in the Categories, then you are unlikely to imagine that there might

be something untoward about singular sentences. After all, in the Categories

it is singular sentences which provide the primary examples of predication.

Thus Simplicius ﬁnds a syllogism in Barbara in the text, and he implicitly

takes singular sentences to express A-predications.

So much the worse, it will be said, for Aristotle—or at least, so much the

worse for many Aristotelians. True, a reference to the Categories may enable us

to understand how they came to treat singular sentences as unproblematical.

But that is only to say that we can understand how they came to make an

egregious error.

Nevertheless, the matter is not quite as simple as that; and I shall ﬁnish

this chapter with a few reﬂections on singular predication.

First, a triﬂing point. Say that a singular sentence is a sentence which

contains at least one singular term, and that a singular term is a term which

designates or refers to an individual item or object. (Proper names are singular

terms, so are many pronouns, so are some phrases of the form ‘the so-and-

so’.) That is approximate, but approximate enough. Then can Aristotelian

syllogistic accommodate singular sentences? Quite evidently it can. Here is

syllogism in Barbara:

156 Predicates and Subjects

Anyone who likes La Boh`eme likes Madama Butterﬂy, and everyone who

likes Butterﬂy likes Tosca.SoanyonewholikesBoh`eme likes Tosca.

That syllogism contains three singular terms, which designate three operas.

There is nothing in the least problematical about that.

There is nothing problematical because the singular terms which occur in

the syllogism are not terms of the syllogism: the syllogism turns around three

A-predications, and in none of those predications is either subject or predicate

a singular term. The predicate in the ﬁrst premiss, for example, is ‘liker of

Madama Butterﬂy’, and that is a general term. In other words, the question

is not: Can Aristotelian syllogistic accommodate singular sentences? For of

course it can. The question is rather this: Can singular terms function as

subjects and predicates in Aristotelian syllogistic? Or: when a sentence which

predicates x in style S of y appears as such as a component in an Aristotelian

syllogism, can either x or y be a singular term?

The Aristotelians certainly took some singular sentences to have, as such, a

subject–predicate form or to say ‘something of something’. To establish that

fact—which is in any case perhaps too evident to need establishment—it is

enough to appeal to a piece of the Prior Analytics which I quoted earlier to

illustrate a different point:

Of all the things which there are, some are such that they are not predicated truly

and universally of anything else (e.g. Cleon, Callias—whatever is individual and

perceptible) but other items are predicated of them (each of the two, after all, is

a man and an animal). Other things are themselves predicated of other items and

yet nothing else is earlier predicated of them. Yet further things both are themselves

predicated of other items and have other items predicated of them (e.g. man of

Callias and animal of man).

(APr 43a25–32)

Alexander, in his long comment on that passage, has this to say:

Individual substances are not themselves truly predicated of other items, but other

items are predicated of them—for the species and genera of individual substances

are predicated of them, and so also are their accidents.

(in APr 291.14–17)⁶⁸

⁶⁸ αἱ δὴ ἄτομοι οὐσίαι αὐταὶ μὲν ἀληθῶς κατ᾿ ἄλλων οὐ κατηγοροῦνται, κατὰ δὲ τούτων

ἄλλα· τὰ γὰρ εἴδη καὶ τὰ γένη τῶν ἀτόμων οὐσιῶν κατηγορεῖται αὐτῶν, ἀλλὰ καὶ τὰ

συμβεβηκότα αὐταῖς.

Singular Predication 157

That seems pretty clear. But there was and is some uncertainty about what

exactly Aristotle meant to deny.

He denies that individuals can ever be predicated truly and universally of

anything else; and he is apparently thinking of afﬁrmative predication. So he

claims that no sentence which predicates an individual term universally and

afﬁrmatively of some other term is true. That, strictly speaking, is all that he

says. But is it all that he means to say? If so, then he leaves open the possibility

that an individual may be predicated truly and universally and negatively of

another item. For example:

No English philosopher is Socrates.

Again, he leaves open the possibility that an individual may be predicated

falsely and universally and afﬁrmatively of another term. For example:

Every philosopher is Socrates.

Again, he leaves open the possibility that an individual may be predicated non-

universally of another term, whether truly or falsely and whether afﬁrmatively

or negatively. For example:

Some philosopher is not Socrates,

Some English philosopher is Socrates.

And ﬁnally, he leaves open the possibility that an individual might be

predicated truly and universally and afﬁrmatively of itself. For example:

Every son of Sophroniscus is Socrates;

or perhaps, more modestly,

EverySocratesisSocrates.

I say that he leaves open such possibilities. The letter of his text certainly

leaves them open. But in the view of some commentators, the spirit of

the text closes them off—what Aristotle in fact intended to convey by his

remarks was that if x is predicated of y, then x is a general and not a singular

term.

After all, if Aristotle had really meant to countenance some cases of singular

predicates, why didn’t he go the whole way and recognize that individuals

may be predicated truly and universally and afﬁrmatively? For if you accept

Every philosopher is Socrates

as well formed but false, then surely you must accept

Every snub-nosed Greek philosopher is Socrates

as well formed and true? But that is an item which Aristotle explicitly

excludes—hence he must have intended to exclude all cases in which singular

terms are predicated.

158 Predicates and Subjects

Perhaps. But I wonder if Aristotle should not, and would not, have

accepted the suggestion that

Every snub-nosed Greek philosopher is Socrates

is well-formed and true. After all, the text of the Analytics does not deﬁnitively

outlaw it. For if ‘Socrates’ is true of everything of which ‘snub-nosed Greek

philosopher’ is true, then there is exactly one snub-nosed Greek philosopher,

and he is Socrates. In that case, ‘snub-nosed Greek philosopher’ is not true

of anything other than Socrates, so that although ‘Socrates’ is predicated

truly and universally and afﬁrmatively of ‘snub-nosed Greek philosopher’,

‘Socrates’ is not thereby predicated truly and universally and afﬁrmatively of

something other than Socrates.

However that may be, the passage from the Analytics is unambiguously

and indisputably clear on one matter: individuals, or singular terms, may be

subjects; and items—at any rate, other items—may be predicated of them.

In other words, the Aristotelian conception of predication is such that you

may predicate ‘animal’ (or animal) of ‘Socrates’ (or of Socrates), just as you

may predicate it of ‘man’ (or of man).

And that indisputable fact has an indisputable corollary: since the Analytics

requires subjects and predicates to be homogeneous, then, whatever he meant

in the passage I have just discussed, Aristotle was in fact committed to the

thesis that singular terms may function as predicates.

That being so, singular sentences may appear as such in Aristotelian

syllogisms—that is to say, there may be syllogisms in which a premiss or

the conclusion predicates x of y and either x or y is a singular term (or

both x and y are singular terms). Indeed, there may be probative syllogisms

which contain singular predications in that way. And Aristotle acknowledges

the fact quite explicitly; for a few lines later in the Prior Analytics he notes

that

it is not possible to prove anything of these items [i.e. of highest genera] save

according to opinion—rather, you prove these of other items. Nor is it possible to

prove individuals of anything else—rather, you prove other items of them.

(APr 43a37–40)⁶⁹

You cannot prove that a singular item holds of some other item or items—you

cannot prove it (let it be added) because it cannot be true. But you can,

⁶⁹ κατὰ μὲν οὖν τούτων οὐκ ἔστιν ἀποδεῖξαι κατηγορούμενον ἕτερον, πλὴν εἰ μὴ κατὰ

δόξαν, ἀλλὰ ταῦτα κατ᾿ ἄλλων· οὐδὲ τὰ καθ ᾿ ἕκαστα κατ᾿ ἄλλων, ἀλλ᾿ ἕτερα κατ᾿ ἐκείνων.

Singular Predication 159

according to Aristotle himself, sometimes prove that x is predicated of y

where y is a singular term. So a singular predication may, as such, form the

conclusion of a syllogism—and hence, of course, a singular predication may

form a premiss of a syllogism.

In fact, several of the examples of proofs in the Posterior Analytics—and

also several of the examples in Galen’s Introduction—concern singular pro-

positions. Nor is there anything remarkable about that: Greek geometers

normally proceeded by ﬁrst proving a singular proposition and then gen-

eralizing it; and in a science such as astronomy it is not easy to avoid

singularities.

The real difﬁculties begin when we ask ourselves in what style of predication

singular terms may feature. For the answer to the question seems to be: In

no style at all. Or rather: In none of the four styles which participate in

Aristotelian syllogisms.

The point may be brought out in the following way. First, singular terms

do not take quantiﬁers. Galen, for one, thinks that it is impossible—perhaps

ungrammatical—to attach quantiﬁers to singular terms:

When we predicate something of Dio, it is not possible to say either all or some.

But when we predicate something of some other object which can be divided—of

man or tree, for example—then it must be determined in the saying whether the

predicate is predicated of all of it or of some (and similarly if it is denied of all or of

some).

(inst log ii 4)⁷⁰

Something similar is found in Alexander: discussing a passage in which the

status of a certain term—indicated in Aristotle’s text simply by the letter

‘C’—is unclear, he remarks that

if it is to universals that the determiners ‘of all’ and ‘of none’ and ‘of some’ and ‘not

of some’ are annexed, as he has shown in the de Interpretatione,thenitisplainthat

the term in question is universal and not individual.

(in APr 65.26–28)⁷¹

⁷⁰ ὅταν μὲν οὖν ἐπὶ ∆ίωνός τι κατηγορῶμεν, οὐκ ἐγχωρεῖ λέγειν οὔτε πᾶς οὔτε τίς· ὅταν

δ᾿ ἐφ᾿ ἑτέρου πράγματος ὃ τέμνεσθαι δύναται, καθάπερ ἐπ᾿ ἀνθρώπου καὶ δένδρου, διωρίσθαι

χρὴ κατὰ τὸν λόγον εἴτε παντὸς αὐτοῦ κατηγορεῖται τὸ κατηγορούμενον εἴτε τινός· ὡσαύτως

δὲ καὶ εἰ παντὸς ἢ τινὸς ἀποφάσκεται.

⁷¹ εἰ γὰρ οἱ διορισμοί, τὸ παντὶ καὶ τὸ μηδενὶ καὶ τὸ τινὶ καὶ τὸ τινὶ μή, τῷ καθόλου

προστίθενται, ὡς ἐν τῷ Περὶ ἑρμηνείας δέδεικται, δῆλον ὡς καθόλου ἐστὶν ὁ ἔσχατος ὅρος

ἀλλ᾿ οὐχὶ ἄτομος.